Question

4. (03.04)

Describe how to determine the average rate of change between x = 1 and x = 3 for the function f(x) = 3x³ +1. Include the average rate of change in your answer. (10 points)

Answer 1

39

Explanation:

The given function to us is ,

`\longrightarrow f(x) = 3x^3 + 1\\`

We need to find the average rate of change between
`x=1` and
`x=3` .

We can calculate the average rate of change as ,

`\longrightarrow A(x) =(f(b)-f(a))/(b-a)`

So that ,

`\longrightarrow A(x) =(f(3)-f(1))/(3-1)\\`

`\longrightarrow A(x) =\frac{ \{ 3(3)^3 +1 -(3(1)^3+1)\}}{2}\\`

`\longrightarrow A(x) = ( 81 +1 - 3 -1 )/(2)\\`

`\longrightarrow A(x) = (78)/(2)\\`

`\longrightarrow\underline{\boxed{ A(x) = 39}}`